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%I #4 Apr 22 2014 01:27:09
%S 1,0,1,3,5,5,11,12,22,26,42,51,79,97,138,179,241,297,410,505,666,824,
%T 1073,1319,1704,2074,2634,3222,4049,4904,6128,7401,9149,11028,13535,
%U 16237,19825,23681,28727,34264,41315,49058,58935,69793,83402,98512,117248
%N Number of partitions p of n such that m(p) = m(c(p)), where m = minimal multiplicity of parts, and c = conjugate.
%F a(n) + 2*A240729(n) = A000041(n) for n >= 1.
%F a(n) + A240729(n) = A240730(n) for n >= 1.
%e a(7) counts these 11 partitions: 61, 511, 43, 421, 4111, 331, 322, 3211, 31111, 2221, 211111, of which the respective conjugates are 5, 31111, 2221, 3211, 4111, 322, 331, 421, 511, 43, 61.
%t z = 30; f[n_] := f[n] = IntegerPartitions[n]; c[p_] := Table[Count[#, _?(# >= i &)], {i, First[#]}] &[p]; m[p_] := Min[Map[Length, Split[p]]];
%t Table[Count[f[n], p_ /; m[p] < m[c[p]]], {n, 1, z}] (* A240729 *)
%t Table[Count[f[n], p_ /; m[p] <= m[c[p]]], {n, 1, z}] (* A240730 *)
%t Table[Count[f[n], p_ /; m[p] == m[c[p]]], {n, 1, z}] (* A240731 *)
%Y Cf. A240727, A240729, A240730, A000041.
%K nonn,easy
%O 1,4
%A _Clark Kimberling_, Apr 11 2014
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